// SPDX-License-Identifier: GPL-2.0-only
/* IEEE754 floating point arithmetic
 * double precision square root
 */
/*
 * MIPS floating point support
 * Copyright (C) 1994-2000 Algorithmics Ltd.
 */

#include "ieee754dp.h"

static const unsigned int table[] = {
        0, 1204, 3062, 5746, 9193, 13348, 18162, 23592,
        29598, 36145, 43202, 50740, 58733, 67158, 75992,
        85215, 83599, 71378, 60428, 50647, 41945, 34246,
        27478, 21581, 16499, 12183, 8588, 5674, 3403,
        1742, 661, 130
};

union ieee754dp ieee754dp_sqrt(union ieee754dp x)
{
        struct _ieee754_csr oldcsr;
        union ieee754dp y, z, t;
        unsigned int scalx, yh;
        COMPXDP;

        EXPLODEXDP;
        ieee754_clearcx();
        FLUSHXDP;

        /* x == INF or NAN? */
        switch (xc) {
        case IEEE754_CLASS_SNAN:
                return ieee754dp_nanxcpt(x);

        case IEEE754_CLASS_QNAN:
                /* sqrt(Nan) = Nan */
                return x;

        case IEEE754_CLASS_ZERO:
                /* sqrt(0) = 0 */
                return x;

        case IEEE754_CLASS_INF:
                if (xs) {
                        /* sqrt(-Inf) = Nan */
                        ieee754_setcx(IEEE754_INVALID_OPERATION);
                        return ieee754dp_indef();
                }
                /* sqrt(+Inf) = Inf */
                return x;

        case IEEE754_CLASS_DNORM:
                DPDNORMX;
                fallthrough;
        case IEEE754_CLASS_NORM:
                if (xs) {
                        /* sqrt(-x) = Nan */
                        ieee754_setcx(IEEE754_INVALID_OPERATION);
                        return ieee754dp_indef();
                }
                break;
        }

        /* save old csr; switch off INX enable & flag; set RN rounding */
        oldcsr = ieee754_csr;
        ieee754_csr.mx &= ~IEEE754_INEXACT;
        ieee754_csr.sx &= ~IEEE754_INEXACT;
        ieee754_csr.rm = FPU_CSR_RN;

        /* adjust exponent to prevent overflow */
        scalx = 0;
        if (xe > 512) {         /* x > 2**-512? */
                xe -= 512;      /* x = x / 2**512 */
                scalx += 256;
        } else if (xe < -512) { /* x < 2**-512? */
                xe += 512;      /* x = x * 2**512 */
                scalx -= 256;
        }

        x = builddp(0, xe + DP_EBIAS, xm & ~DP_HIDDEN_BIT);
        y = x;

        /* magic initial approximation to almost 8 sig. bits */
        yh = y.bits >> 32;
        yh = (yh >> 1) + 0x1ff80000;
        yh = yh - table[(yh >> 15) & 31];
        y.bits = ((u64) yh << 32) | (y.bits & 0xffffffff);

        /* Heron's rule once with correction to improve to ~18 sig. bits */
        /* t=x/y; y=y+t; py[n0]=py[n0]-0x00100006; py[n1]=0; */
        t = ieee754dp_div(x, y);
        y = ieee754dp_add(y, t);
        y.bits -= 0x0010000600000000LL;
        y.bits &= 0xffffffff00000000LL;

        /* triple to almost 56 sig. bits: y ~= sqrt(x) to within 1 ulp */
        /* t=y*y; z=t;  pt[n0]+=0x00100000; t+=z; z=(x-z)*y; */
        t = ieee754dp_mul(y, y);
        z = t;
        t.bexp += 0x001;
        t = ieee754dp_add(t, z);
        z = ieee754dp_mul(ieee754dp_sub(x, z), y);

        /* t=z/(t+x) ;  pt[n0]+=0x00100000; y+=t; */
        t = ieee754dp_div(z, ieee754dp_add(t, x));
        t.bexp += 0x001;
        y = ieee754dp_add(y, t);

        /* twiddle last bit to force y correctly rounded */

        /* set RZ, clear INEX flag */
        ieee754_csr.rm = FPU_CSR_RZ;
        ieee754_csr.sx &= ~IEEE754_INEXACT;

        /* t=x/y; ...chopped quotient, possibly inexact */
        t = ieee754dp_div(x, y);

        if (ieee754_csr.sx & IEEE754_INEXACT || t.bits != y.bits) {

                if (!(ieee754_csr.sx & IEEE754_INEXACT))
                        /* t = t-ulp */
                        t.bits -= 1;

                /* add inexact to result status */
                oldcsr.cx |= IEEE754_INEXACT;
                oldcsr.sx |= IEEE754_INEXACT;

                switch (oldcsr.rm) {
                case FPU_CSR_RU:
                        y.bits += 1;
                        fallthrough;
                case FPU_CSR_RN:
                        t.bits += 1;
                        break;
                }

                /* y=y+t; ...chopped sum */
                y = ieee754dp_add(y, t);

                /* adjust scalx for correctly rounded sqrt(x) */
                scalx -= 1;
        }

        /* py[n0]=py[n0]+scalx; ...scale back y */
        y.bexp += scalx;

        /* restore rounding mode, possibly set inexact */
        ieee754_csr = oldcsr;

        return y;
}